There does not appear to be an article dedicated to Hylomorphism in the Stanford Encyclopedia of Philosophy, though Aristotle's Metaphysics by S. Mark Cohen (Stanford: Aristotle's Metaphysics) discussed the topic in Sections 7 (Substance and Essence) and 8 (Substances as Hylomorphic Compounds).

Aristotle defines X's matter as "that out of which" X is made. For example, letters are the matter of syllables. Thus, "matter" is a relative term: an object counts as matter relative to something else. For example, clay is matter relative to a brick because a brick is made of clay, whereas bricks are matter relative to a brick house.

Change is analyzed as a material transformation: matter is what undergoes a change of form. For example, consider a lump of bronze that's shaped into a statue. Bronze is the matter, and this matter loses one form (that of a lump) and gains a new form (that of a statue).

Aristotle applies his theory of hylomorphism to living things. He defines a soul as that which makes a living thing alive. Life is a property of living things, just as knowledge and health are. Therefore, a soul is a form — that is, a property or set of properties — belonging to a living thing. Furthermore, Aristotle says that a soul is related to its body as form to matter.

Hence, Aristotle argues, there is no problem in explaining the unity of body and soul, just as there is no problem in explaining the unity of wax and its shape. Just as a wax object consists of wax with a certain shape, so a living organism consists of a body with the property of life, which is its soul. On the basis of his hylomorphic theory, Aristotle rejects the Pythagorean doctrine of reincarnation, ridiculing the notion that just any soul could inhabit just any body.

It is unclear whether Aristotle identifies the soul with the body's structure. According to one interpretation of Aristotle, a properly organized body is already alive simply by virtue of its structure. However, according to another interpretation, the property of life — that is, the soul — is something in addition to the body's structure. Likewise, according to this second interpretation, a living body is alive not only because of its structure but also because of an additional property: the soul is this additional property, which a properly organized body needs in order to be alive. John Vella uses Frankenstein's monster to illustrate the second interpretation: the corpse lying on Frankenstein's table is already a fully organized human body, but it is not yet alive; when Frankenstein activates his machine, the corpse gains a new property, the property of life, which Aristotle would call the soul.